A problem familiar to every engineer is that many physical quantities cannot be measured directly. Instead, the response g(x) of a measurement system, such as a sensor, to physical quantities x is measured. Here, the term “sensor” refers to any system with response g(x) to a physical quantity x. For an optical system, the “sensor” may be any combination of lenses, mirrors, prisms, filters and physical sensing elements that comprise the imaging system. Thus, the relationship between the physical quantity and the response function for the sensor may not be linear. For best results, the sensor must be calibrated by linearizing the reponse to produce the calibrated output. Calibration requires the determination of the inverse of g.
Typically, calibration functions are determined by providing the sensor with a series of known inputs xi while recording the corresponding output of the measurement system gi. This approach works well if the system response g(x) is very nearly linear or of low order, and the system can be excited with accurate knowledge of xi. If g(x) is not well characterized by a low-order function, a direct calibration will require a substantial number of calibration pairs (g(xi),xi) to establish the local variations of g. Furthermore, the requirement to know the input x accurately is not always practical. Thus, there remains a need for an easier way to calibrate a sensor.